2d:null 2e:["$","title",null,{"children":"Expression | Vinícius Mello | Observable"}] 33:T31cc,Ex = { let symtab = {}; let stack = [symtab]; class Ex { static makeSymbol(name) { const sym = new Ex(); sym.head = Ex.Symbol; sym.tail = [name]; sym.up = []; sym.down = []; stack[stack.length-1][name] = sym; return sym; } static push() { stack.push({}); } static pop() { stack.pop(); } static getSymbol(name) { for(let i = stack.length-1;i>=0;--i) { if(stack[i][name]!==undefined) { return stack[i][name]; } } } isBlank() { return this.head === Ex.Blank || this.head === Ex.BlankSequence || this.head === Ex.BlankNullSequence; } isAtom() { return this.head === Ex.Symbol || this.head === Ex.Integer || this.head === Ex.Rational || this.head === Ex.String; } constructor(ex, vars = {}) { if(ex===undefined) { return; } if(typeof(ex) === 'number' && Number.isInteger(ex)) { this.head = Ex.Integer; this.tail = [ex]; return; } if(typeof(ex) === 'object') { this.head = ex.head; this.tail = ex.tail; return; } function traverse(node) { // console.log(node.type, node.fn, node.value, node.args); switch(node.type) { case 'OperatorNode': switch(node.fn) { case 'add': { const a = traverse(node.args[0]); const b = traverse(node.args[1]); return new Ex('Plus(a,b)', {a,b}); } break; case 'multiply': { const a = traverse(node.args[0]); const b = traverse(node.args[1]); return new Ex('Times(a,b)', {a,b}); } break; case 'pow': { const a = traverse(node.args[0]); const b = traverse(node.args[1]); return new Ex('Power(a,b)', {a,b}); } break; case 'subtract': { const a = traverse(node.args[0]); const b = traverse(node.args[1]); return new Ex('Plus(a,Times(mo,b))', {a, mo: Ex.minusOne, b}); } break; case 'unaryMinus': { const a = traverse(node.args[0]); return new Ex('Times(mo,a)', {mo: Ex.minusOne, a}); } break; case 'divide': { const a = traverse(node.args[0]); const b = traverse(node.args[1]); return new Ex('Times(a,Power(b,mo))',{a, mo: Ex.minusOne, b}); } break; } break; case 'ParenthesisNode': return traverse(node.content); break; case 'FunctionNode': { const tail = node.args.map((n)=> traverse(n)); return new Ex({head: Ex.getSymbol(node.fn.name), tail: tail}); } break; case 'SymbolNode': { const sp = node.name.split('_'); if(sp.length==1) { if(vars[node.name]!==undefined) { return vars[node.name]; } return Ex.getSymbol(node.name); } else if(sp.length==2) { const str = new Ex({head: Ex.String, tail: [sp[0]]}); if(sp[1] === "") return new Ex({head: Ex.Blank, tail: [str] }); return new Ex({head: Ex.Blank, tail: [str, Ex.getSymbol(sp[1])] }); } else if(sp.length==3) { const str = new Ex({head: Ex.String, tail: [sp[0]]}); if(sp[2] === "") return new Ex({head: Ex.BlankSequence, tail: [str] }); return new Ex({head: Ex.BlankSequence, tail: [str, Ex.getSymbol(sp[2])] }); } else if(sp.length==4) { const str = new Ex({head: Ex.String, tail: [sp[0]]}); if(sp[3] === "") return new Ex({head: Ex.BlankNullSequence, tail: [str] }); return new Ex({head: Ex.BlankNullSequence, tail: [str, Ex.getSymbol(sp[3])] }); } } break; case 'ConstantNode': return new Ex(node.value); break; } } let pex = math.parse(ex); let {head, tail} = traverse(pex); this.head = head; this.tail = tail; } equal(ex) { // console.log('equal:',this.toString(), ex.toString()); if(this.head !== ex.head) return false; if(this.isAtom() && ex.isAtom()) { for(let i=0; i=0 && n>=0) { if(this.tail[m].equal(ex.tail[n])) { m = m-1; n = n-1; } else { return this.tail[m].comp(ex.tail[n]); } } return m < n; } // O4 if(this.head === Ex.Power && ex.head === Ex.Power) { if(this.tail[0].equal(ex.tail[0])) { return this.tail[1].comp(ex.tail[1]); } else { return this.tail[0].comp(ex.tail[0]); } } // O6 if(this.head === ex.head) { let m = this.tail.length; let n = ex.tail.length; let i = 0; while(i (a.comp(b) ? -1 : 1)); } ex = new Ex({head: this.head, tail: ex}); let tex; for(let i=0;i { let cap = {}; if(ex.match(rule, cap)) { return fn(cap); } return null; }); } toString() { if(this.head === Ex.Blank) { return this.tail[0].tail[0]+'_'+(this.tail[1] !== undefined ? this.tail[1].toString() : '' ); } if(this.head === Ex.BlankSequence) { return this.tail[0].tail[0]+'__'+(this.tail[1] !== undefined ? this.tail[1].toString() : '' ); } if(this.head === Ex.BlankNullSequence) { return this.tail[0].tail[0]+'___'+(this.tail[1] !== undefined ? this.tail[1].toString() : '' ); } if(this.head === Ex.Rational) { return this.tail[0]+'/'+this.tail[1]; } if(this.isAtom()) return this.tail[0].toString(); let r = this.head.toString()+'('; let t = this.tail.map((e) => e.toString()); return r+t.toString()+')'; } } Ex.Symbol = Ex.makeSymbol('Symbol'); Ex.Symbol.head = Ex.Symbol; Ex.Integer = Ex.makeSymbol('Integer'); Ex.Rational = Ex.makeSymbol('Rational'); Ex.String = Ex.makeSymbol('String'); Ex.Plus = Ex.makeSymbol('Plus'); Ex.Plus.orderless = true; Ex.Plus.flat = true; Ex.Times = Ex.makeSymbol('Times'); Ex.Power = Ex.makeSymbol('Power'); Ex.Sequence = Ex.makeSymbol('Sequence'); Ex.Blank = Ex.makeSymbol('Blank'); Ex.BlankSequence = Ex.makeSymbol('BlankSequence'); Ex.BlankNullSequence = Ex.makeSymbol('BlankNullSequence'); Ex.Sqrt = Ex.makeSymbol('Sqrt'); Ex.Sqrt.addRule('Sqrt(a_)', (cap)=> new Ex('Power(a,Rational(1,2))', cap)); Ex.minusOne = new Ex(-1); return Ex; }34:[] 31:{"id":"850d02d248ce96e5","slug":"expression","title":"Expression","thumbnail":"732b7f3be105bc91f9ceda9e7ee9e9d2a54494516c38edf34e755302de384a61","access_level":"public","create_time":"$D2020-07-26T10:22:28.704Z","update_time":"$D2020-07-28T22:28:36.319Z","view_time":null,"first_public_time":"$D2020-07-27T00:01:58.548Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"7a4ecd430a93cd6f","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":"starter_2024"},"version":267,"publish_version":267,"role":null,"authored":false,"authors":[{"type":"individual","id":"ecc4854ab7ad95b6","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":null}],"members":[{"type":"individual","id":"ecc4854ab7ad95b6","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Expression","cells":[{"id":0,"value":"md`# Expression`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"$33","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"{\n const ex = (new Ex('Plus(4,3,Rational(7,2),Sqrt(2),Plus(4,2))')).eval();\n \n return ex.toString();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"math = require('mathjs');","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 32:"$31:body"